One-step, split sample estimator for E[Y(t)], E[Y(t)|R=0], under sensitivity analysis for exchangability assumption

est_psi_exchange(
  Y,
  M,
  R,
  X,
  t,
  trt,
  gamma,
  fold,
  seed,
  IF_output,
  simple_trunc,
  quant,
  kernel,
  method = "optim",
  single_index_method,
  use_mave = TRUE,
  s_t_y = NULL
)

Arguments

Y: Numeric outcome vector. Missing values are internally replaced with 0 prior to model fitting.
M: Binary indicator for observed outcome (1 = observed, 0 = missing).
R: Binary group indicator used to stratify nuisance and outcome models.
X: Data frame or matrix of baseline covariates.
t: Treatment assignment vector.
trt: Treatment level for which the target estimand is computed.
gamma: Numeric vector of sensitivity parameters.
fold: Number of cross-fitting folds.
seed: Optional integer random seed for fold assignment. Use NULL to leave RNG state unchanged.
IF_output: Logical; if TRUE, include influence-function vectors in the returned list.
simple_trunc: Logical; if TRUE, apply quantile truncation to inverse probability weights. If FALSE, apply IF truncation diagnostics.
quant: Numeric in (0, 1) used as the upper quantile for simple weight truncation when simple_trunc = TRUE.
kernel: Characters; Kernel used for SIMs. K2_Biweight for Epanechnikov kernel, dnorm for Gaussian kernel.
method: Characters; Optimization method used for SIMs. Choices are: optim, nlminb, nmk. Note that method is set to optim if single_index_method=norm1coef.
single_index_method: Characters; Three implementations for SIMs: fixed_bandwidth for setting bandwidth to 1, fixed_coef for setting the first coefficient to 1, and norm1coef for setting the norm of coefficients to 1.
use_mave: Logical; if TRUE, use Minimum Average Variance Estimation (MAVE) method for initial coefficients value for SIMs. If FALSE, use sliced inverse regression. Default is TRUE.
s_t_y: A function of Y in the exponential tilting model. If NULL, s_t_y is set to pnorm((y

Value

A named list of estimates and uncertainty summaries for each value in gamma. Core elements include point estimates (est, est_R0), variance estimates (var, var_R0), and confidence interval bounds (lowerCI*, upperCI*). Additional components depend on simple_trunc and IF_output:

simple_trunc = TRUE: returns quantile-weight-truncated summaries only.
simple_trunc = FALSE: additionally returns truncated summaries and truncated IF objects when requested.
IF_output = TRUE: includes influence-function lists (IF*) and, when relevant, truncated IF lists (IF_trunc*).

Examples

# out <- est_psi_exchange(Y, M, R, X, t, trt = 1, gamma = c(0, 0.5),
#                         fold = 5, seed = 1, IF_output = FALSE,
#                         simple_trunc = TRUE, quant = 0.99, kernel="dnorm", 
#                         single_index_method="norm1coef", method="optim")